The 35-year-old went 12-8 with a 3.38 ERA in 2012 with the Chicago Cubs and Texas Rangers, and is 124-124 for his 15-year career.

Dempster had spent his entire career in the National League before Texas acquired him at last year’s trade deadline. He went 7-3 with a 5.09 ERA with the Rangers, but lost his final start of the season after allowing five runs over three innings to the Oakland Athletics. Because of the loss, Texas did not clinch the AL West and had to settle for the Wild Card.

While he made two different trips to the disabled list in 2012, Dempster had been a durable starter since 2008, logging four straight 200-inning seasons before hurling 173 innings in 2012.

Rosenthal notes that Dempster is seeking a three-year deal, and reportedly turned down a two-year, $26-million offer from Boston earlier in the off-season.

While Dempster has been more than serviceable the last few seasons, Boston may be better served spending the money elsewhere on a younger starter. A few options that remain on the free agent market include Anibal Sanchez (28) and Shawn Marcum (30).